How would you simplify $\sqrt{7} (3 - \sqrt{7}) + 8 \sqrt{7}$ $sqrt 7 (3-sqrt 7)+8 sqrt7$ ?

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How would you simplify $\sqrt{7} (3 - \sqrt{7}) + 8 \sqrt{7}$ $sqrt 7 (3-sqrt 7)+8 sqrt7$ ?

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Answer 1 · 2016-03-15T19:30:16

$11 \sqrt{7} - 7$ $11sqrt(7)-7$

Explanation:

$1$ $1$ . Distribute the $\sqrt{7}$ $sqrt(7)$ to each term in the brackets.

$\sqrt{7} (3 - \sqrt{7}) + 8 \sqrt{7}$ $color(red)(sqrt(7))(3-sqrt(7))+8sqrt(7)$

$= \sqrt{7} \cdot 3 - \sqrt{7 \cdot 7} + 8 \sqrt{7}$ $=color(red)(sqrt(7))*3-sqrt(7color(red)(*7))+8sqrt(7)$

$= 3 \sqrt{7} - 7 + 8 \sqrt{7}$ $=3sqrt(7)-7+8sqrt(7)$

$2$ $2$ . Since radicals are like variables, you can think of $\sqrt{7}$ $color(blue)(sqrt(7))$ in $3 \sqrt{7}$ $3color(blue)(sqrt(7))$ as a $variable$ $color(blue)("variable")$ . Thus, add $8 \sqrt{7}$ $8sqrt(7)$ to $3 \sqrt{7}$ $3sqrt(7)$ .

$= 3 \sqrt{7} + 8 \sqrt{7} - 7$ $=3sqrt(7)+8sqrt(7)-7$

$=color(green)(|bar(ul(color(white)(a/a)11sqrt(7)-7color(white)(a/a)|)))$

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How would you simplify $\sqrt{7} (3 - \sqrt{7}) + 8 \sqrt{7}$ $sqrt 7 (3-sqrt 7)+8 sqrt7$ ?

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How would you simplify sqrt 7 (3-sqrt 7)+8 sqrt7√7(3−√7)+8√7sqrt 7 (3-sqrt 7)+8 sqrt7?

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How would you simplify $\sqrt{7} (3 - \sqrt{7}) + 8 \sqrt{7}$ $sqrt 7 (3-sqrt 7)+8 sqrt7$ ?